A characterization of generalized exponential polynomials in terms of\n decomposable functions

2018/12/16 by Miklós Laczkovich, Laczkovich, Miklos
Mathematics · #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1812.06434

Abstract

Let G be a topological commutative semigroup with unit. We prove that a\ncontinuous function f colon G\→ cc is a generalized exponential polynomial\nif and only if there is an n\≥ 2 such that f(x₁ +\… +x_n ) is\ndecomposable; that is, if f(x₁ +\… +x_n )= sumik u_i cd v_i, where the\nfunction u_i only depends on the variables belonging to a set emp \≠ E_i\n subsetneq x₁ stb x_n , and v_i only depends on the variables\nbelonging to x₁ stb x_n se E_i (i=1 stb k).\n

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